Noncommutative Riemann Surfaces

@inproceedings{Arnlind2008NoncommutativeRS,
  title={Noncommutative Riemann Surfaces},
  author={Joakim Arnlind and Martin Bordemann and Laurent Hofer and Jens Hoppe and Hidehiko Shimada},
  year={2008}
}
We introduce C-Algebras of compact Riemann surfaces Σ as non-commutative analogues of the Poisson algebra of smooth functions on Σ. Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, nicely interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C… CONTINUE READING